Suppose there are 2 defectives among 5

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In a scenario with 2 defectives among 5 items, it is established that a maximum of 3 tests is needed to identify both defectives. The discussion focuses on calculating the probability of finding the first defective on the first test, given that the second defective is found on the third test. Participants are encouraged to show their calculations and reasoning to clarify their understanding and address any difficulties. The conversation emphasizes the importance of logical reasoning in probability and testing strategies. Overall, the thread aims to solve the problem through collaborative analysis and mathematical exploration.
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suppose there are 2 defectives among 5...

suppose there are 2 defectives among 5, test one at a time until you find the 2nd defective, find:

1.you need at most 3 tests
2.given the 2nd defective found at 3rd test, find the p that you find the 1st defective at 1st test.

Thanks.
 
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shinkansenfan said:
suppose there are 2 defectives among 5, test one at a time until you find the 2nd defective, find:

1.you need at most 3 tests
2.given the 2nd defective found at 3rd test, find the p that you find the 1st defective at 1st test.

Thanks.

Forum rules require you to show your work. Tell us what you have done so far, and where you are stuck.

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Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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